1. Field of the Invention
The present invention relates generally to methods and apparatus for rendering digital objects and, more specifically, to methods for identifying polygons that are back facing relative to a reference point and for culling the data of such back facing polygons prior to rendering. In particular, the methods and apparatus of the present invention decide whether to cull data for a particular polygon after the vertices of that polygon have been sorted to facilitate the accelerated processing of the polygons.
2. Background of the Related Art
As is well known in the art, computers typically break three-dimensional objects down into a series of polygons (e.g., triangles), which together make up the outer surfaces of the three-dimensional object. The relative positions of each of the polygons of a three-dimensional object are typically stored and manipulated in digital form; i.e., a series of 0's and 1's that indicates the relative locations of the polygons to one another on the three-dimensional object, as well as the positions, or locations (i.e., x-, y-, and z-coordinates), of the vertices of each polygon of the three-dimensional object. Accordingly, for purposes of this disclosure, the digital form of a three-dimensional object is referred to as a “digital object”.
The data for each polygon of a digital object typically includes positional data for at least three vertices of the polygon along two adjacent edges. If the polygon is a triangle, the digital make-up of the triangle includes positional data for all three vertices of the triangle. Typically, the positional data for the vertices of each polygon of the digital object are arranged in the same orientation, or order. For example, the positional data for the vertices of all of the polygons of a digital object may be ordered around the peripheries of the polygons in a clockwise (CW) orientation or in a counter-clockwise (CCW) orientation.
In addition to breaking a three-dimensional object down to data representative of the vertices of a collection of polygons having specific relative positions, characteristic data (e.g., color, shading, texture) for the entire three-dimensional object, for a portion thereof, or for each polygon or a small set of polygons may also be stored and processed in digital form.
When viewed from a specific reference point, such as from the viewpoint of a computer user looking at a video monitor or from one looking at an image on paper, a digital three-dimensional object is shown in two dimensions. Typically, only the portions of the digital object that face, or that are visible from, the reference point are shown. These portions of the digital object are the so-called “front facing” polygons of the digital object. This is true both when the digital object is in a stationary position and when the digital object is being moved or manipulated.
Polygons of a digital object that do not face the reference point are typically referred to as “back facing” polygons. Relative to the reference point, the vertices of a back facing polygon have an orientation that is opposite the actual orientation of the vertices of that polygon. For example, if a polygon with CW-oriented vertices is back facing, the vertices will appear, from the reference point, to have a CCW orientation.
As back facing polygons of a digital object do not face a reference point, such as a viewer, back facing polygons are typically not displayed to the viewer. Accordingly, prior to rendering each synthesized, or rendered, image (i.e., each particular orientation or state), or scene, of the digital object, the other, non-visible, back facing polygons of the digital object are typically culled, or eliminated from further processing until an image of the digital object has been rendered. By culling data for back facing polygons, rendering of an image of the digital object will be accelerated.
Prior to rendering an image of the digital object, the positional data for the vertices of a polygon are typically evaluated to determine whether, relative to the reference point of a viewer, the polygon is front facing or back facing.
Once the polygons of an image or scene of a digital object are transformed into the viewer's perspective (i.e., a two-dimensional image), the sign (S) of the z-axis term of the cross product, or cross product term (CPT), of two edges of each transformed polygon will indicate the orientation of vertices of the polygon (e.g., whether the transformed polygon has a CW or CCW orientation). For example, if the vertices of a polygon are oriented CW, the actual, or original, sign bit (S0) is a “1”. If the vertices of a polygon are oriented CCW, the actual, or original, sign bit (S0) is a “0”. This sign bit is then used to compare the (two-dimensional) position of each polygon in the image to be rendered to its actual, or original, orientation on the object (its two-dimensional orientation when front facing). If these orientations are not equal, the polygon is determined to be a back facing polygon and the data is culled from the rendering process.
A example of a conventional method for back face culling includes selecting the vertices, V0, V1, and V2, along two adjoined edges of each polygon. For purposes of this disclosure, V0, V1, and V2 refer to the order in which the positional data for the vertices of a polygon are introduced into a rendering application; these designations do not necessarily refer to the order in which vertices are located around the periphery of the polygon. The two-dimensional x-axis and y-axis positions of each of the vertices of a polygon of a digital object to be displayed or otherwise output are then determined, with V0.x, V1.x, and V2.x being the respective x-axis positions of vertices V0, V1, and V2 and V0.y, V1.y, and V2.y being the respective y-axis positions of vertices V0, V1, and V2. The differences between the x-axis and y-axis positions of each of the selected vertices are then determined, for example, as follows:                X10=V1.x−V0.x;        Y12=V1.y−V2.y;        X12=V1.x−V2.x; and        Y10=V1.y−V0.y.The cross product term for the polygon is then calculated, as follows:CPT=(X10×Y12)−(X12×Y10).Assuming that the digital order in which the positional data for the analyzed vertices, V0, V1, and V2, are arranged remains unchanged from the order in which the positional data for these vertices was introduced into the rendering application, the sign (S) of the CPT (S=sign (CPT)) is then used to determine whether or not the data for the analyzed polygon should be culled prior to rendering. If the actual orientation of the vertices of the polygon was CW (i.e., S0=1) and S=0, the analyzed polygon is back facing and, accordingly, the positional data for that polygon is culled. Alternatively, if the actual orientation of vertices of the polygon was CCW (i.e., S0=0) and S=0, the positional data for the vertices of the polygon is retained for rendering purposes, as the polygon is front facing relative to the reference point and the polygon will be shown when the digital object is displayed or otherwise output.        
In rendering a two-dimensional image of a three-dimensional digital object, it is often necessary to sort the vertices of each polygon. For example, the positional data for the vertices of a particular polygon of the digital object may be introduced into the rendering application in a particular order, which is then changed, such as in a triangle setup operation, to facilitate rendering of the polygon. Accordingly, the positional data for the various vertices of the polygon may be re-ordered, or shuffled, which will change a CPT that is based on the order in which the positional data for the vertices is presented. Thus, while conventional methods for culling back facing polygons decrease the amount of time necessary to render an image of a digital object, the vertex differences or CPT's calculated by these methods cannot be reliably reused for subsequent rendering operations, such as polygon characterization processes (e.g., determining the coloration, shadowing, or texturing of a polygon). As a consequence, the vertex differences or CPT's must be recalculated once sorting has occurred.
Moreover, if the positional data for the vertices of a particular polygon are sorted prior to determining the vertex differences or CPT's, without having the positional data for each vertex tied to an indicator of the position of the vertex on the polygon, the sign of a subsequently calculated CPT could provide incorrect information about whether the polygon is front facing or back facing.
No known prior art method or apparatus uses a CPT obtained by evaluating sorted vertices that can be used in analyzing polygons of a graphic image and determining whether to cull data representative of each analyzed polygon. Similarly, no known method or apparatus is used for calculating a CPT that may be used both in decisions to cull back facing polygons of a digital object and in subsequent rendering operations.